A wide-area positioning system, such as the Global Positioning System (GPS), uses a constellation of satellites to position or navigate objects on earth. Each satellite in the GPS system currently transmits two carrier signals, L1 and L2, with frequencies of 1.5754 GHz and 1.2276 GHz, and wavelengths of 0.1903 m and 0.2442 m, respectively. Next generation Global Navigation Satellite Systems (GNSS), such as the modernized GPS and Galileo systems, will offer a third carrier signal, L5. In the GPS system, L5 will have a frequency of 1.1765 GHz, and a wavelength of 0.2548 m.
Two types of GPS measurements are usually made by a GPS receiver: pseudorange measurements and carrier phase measurements.
The pseudorange measurement (or code measurement) is a basic GPS observable that all types of GPS receivers can make. It utilizes the C/A or P codes modulated onto the carrier signals. With the GPS measurements available, the range or distance between a GPS receiver and each of a plurality of satellites is calculated by multiplying a signal's travel time (from the satellite to the receiver) by the speed of light. These ranges are usually referred to as pseudoranges because the GPS measurements may include errors due to various error factors, such as satellite clock timing error, ephemeris error, ionospheric and tropospheric refraction effects, receiver tracking noise and multipath error, etc. To eliminate or reduce these errors, differential operations are used in many GPS applications. Differential GPS (DGPS) operations typically involve a base reference GPS receiver, a user GPS receiver, and a communication mechanism between the user and reference receivers. The reference receiver is placed at a known location and is used to generate corrections associated with some or all of the above error factors. Corrections generated at the reference station, raw data measured at the reference station, or corrections generated by a third party (e.g., a computer or server) based on information received from the reference station (and possibly other reference stations as well) are supplied to the user receiver, which then uses the corrections or raw data to appropriately correct its computed position.
The carrier phase measurement is obtained by integrating a reconstructed carrier of the signal as it arrives at the receiver. Because of an unknown number of whole cycles in transit between the satellite and the receiver when the receiver starts tracking the carrier phase of the signal, there is a whole-cycle ambiguity in the carrier phase measurement. This whole-cycle ambiguity must be resolved in order to achieve high accuracy in the carrier-phase measurement. Whole-cycle ambiguities are also known as “integer ambiguities” after they have been resolved, and as “floating ambiguities” or “real-valued ambiguities” prior to their resolution. The terms “ambiguity” and “ambiguities” refer to variables (i.e., variables representing whole cycle ambiguities) whose values are to be resolved, while the terms “ambiguity values,” “integer ambiguity values” and “floating ambiguity values” refer to values that have been computed or determined for respective ambiguities. Differential operations using carrier-phase measurements are often referred to as real-time kinematic (RTK) positioning/navigation operations.
When GPS signals are continuously tracked and no loss-of-lock occurs, the integer ambiguities resolved at the beginning of a survey can be kept for the entire GPS kinematic positioning span. The GPS satellite signals, however, may be occasionally shaded (e.g., due to buildings in “urban canyon” environments), or momentarily blocked (e.g. when the receiver passes under a bridge or through a tunnel). Generally in such cases, the integer ambiguity values are “lost” and must be re-determined. This process can take from a few seconds to several minutes. In fact, the presence of significant multipath errors or unmodeled systematic biases in one or more measurements of either pseudorange or carrier phase may make it impossible with present commercial GPS RTK systems to resolve the ambiguities. As the receiver separation (i.e., the distance between a reference receiver and a mobile receiver whose position is being determined) increases, distance-dependent biases (e.g. orbit errors and ionospheric and tropospheric effects) grow, and, as a consequence, reliable ambiguity resolution (or re-initialization) becomes an even greater challenge.